Abstract
The nature of basic differential equations governing the concentration of substrate and product species in a reaction of maltose catalyzed by sacchariying α-amylase from B. subtilis was investigated by analyzing their behavior near zero time. Near zero time, the differential equations could be approximated by simultaneous linear differential equations with respect to time. A characteristic equation was formulated from the coefficient matrix, and the eigen values, which are functions of initial maltose concentration and kinetic constants, were calculated. The eigen values were found to be negative real numbers except for one eigen value. This one eigen value had a negative real value at low maltose concentrations and a positive one at high concentrations.
Threshold concentration was defined as the initial maltose concentration at which the eigen value had zero value. The concentration was estimated to be 38.2mM. Above the threshold concentration, the concentrations of oligomers having chains longer than maltose increased explosively at the initial stage of reaction and the concentrations at the steady state increased sharply with increase of substrate concentration, showing a typical threshold phenomenon. This type of threshold phenomenon may not necessarily be characteristic of this enzyme. Enzymes which have activities for both degradation and synthesis may also show a threshold phenomenon.
